Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-6x-3y &= 3 \\ 7x+4y &= -6\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $4y = -7x-6$ Divide both sides by $4$ to isolate $y$ $y = {-\dfrac{7}{4}x - \dfrac{3}{2}}$ Substitute this expression for $y$ in the first equation. $-6x-3({-\dfrac{7}{4}x - \dfrac{3}{2}}) = 3$ $-6x + \dfrac{21}{4}x + \dfrac{9}{2} = 3$ Simplify by combining terms, then solve for $x$ $-\dfrac{3}{4}x + \dfrac{9}{2} = 3$ $-\dfrac{3}{4}x = -\dfrac{3}{2}$ $x = 2$ Substitute $2$ for $x$ back into the top equation. $-6( 2)-3y = 3$ $-12-3y = 3$ $-3y = 15$ $y = -5$ The solution is $\enspace x = 2, \enspace y = -5$.